The study found that the vast majority of American families are bringing in more money than their parents did, adjusted fror inflation, than when they were the same age. But especially among the most poor, bigger paychecks aren't often enough to push families up the income ladder.

Most people raised in very rich and very poor households didn’t see their own circumstances change much when they grew up. The report found that 70 percent of Americans whose parents were in the bottom fifth of the income ladder stayed below the middle as adults. And 63 percent of those born in the top fifth of the income ladder stayed above the middle when they became adults.

Those born in the middle three-fifths of the income spectrum did have a higher likelihood of moving either up or down the ladder as adults.

In all, 35 percent of American households could be classified as upwardly mobile, meaning they had a higher household income than their parents at the same age and were at a higher point in the income distribution ladder than their parents had been.

People can make more money than their parents and still not rise up the income ladder because median income has increased at all levels.

Currier said that means many people may feel more successful than their parents – maybe because they own a slightly bigger house or have a flat-screen TV – but aren’t much better off relative to other households today.

"The general public thinks there’s much more mobility than there actually is," said Lawrence Mishel, president of the Economic Policy Institute, who was not involved in the research.

Mishel also noted that many households have more income than their parents did at the same age because more women are working than in the previous generation.

That's a contributing factor that the Pew report also acknowledged. Looking more narrowly just at men, they found that 59 percent of sons are earning more than their dads did at the same age.

The Pew analysis was based on the Panel Study of Income Dynamics, an in-depth look at family finances, using data from 1968 through 2009. The long-running study allowed the researchers to compare how adults are doing in comparison to how their parents were doing at the same point in their lives. The figures were adjusted for inflation, family size and age.

A separate look at total wealth found that half of Americans are wealthier than their parents were at the same age.

The fact that most households are bringing in more income than their parents but only half are wealthier is a little troubling, Currier said.

“Clearly families do have more money in terms of what’s coming in every month, but they don’t have greater savings, they don't have greater assets - for the most part - than their parents did,” she said.

One of the biggest ways individuals can improve their circumstances relative to their parents is to get a college degree.

The researchers found that a four-year degree triples a person’s chances of making it from the bottom to the top of the income ladder. College graduates also were more likely to be doing better than their parents were at the same age, in terms of both income and wealth.

The researchers also found that African-Americans were less likely than whites to outearn their parents. The data was too limited to do a similar analysis of other racial and ethnic minorities.